Unemployment Risks and Intra-Household Insurance

We consider an economy with incomplete markets and intra-household risk sharing, where households are formed by a job-seeker and an employed spouse and differ by the productivity of the spouse. We study the constrained efficient private provision of insurance within the household through the labor supply of the spouse, and what unemployment risks should be publicly insured away. Unlike the spouse's total income, neither productivity nor labor supply is observed. We characterize the directed search equilibrium, and show that the spouse's labor supply is negatively affected by unemployment benets regardless of the search outcome of the worker in line with the empirical evidence. We also show that the optimal unemployment benefits are contingent on the household's total income as it affects the trade-off between consumption-smoothing and job search incentives. Moreover, we numerically explore the welfare gains of implementing a household-income-based unemployment insurance.